# Distribution theory

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I need help understanding the problems attached. I need solutions along with explanations. Just solutions will not help me understand.

Let the random variable Y_n have a distribution this is b(n,p).

a) Prove that Y_n/n converges in probability p. This result is one form of the weak law of large numbers.

b) Prove that 1 - Y_N/n converges in probability to 1 - p.

c) Prove that Y_n/n)(1 - Y_n/n) converges in probability to p(1 -p).

let W_n denote a random variable with mean u and variance b/n^p, where p . 0, u, and b are constants (not functions of n). Prove that W_n converges in probability to u.... (please see the attached file)

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#### Solution Summary

This solution explains some distribution theory problems.